Several symbolic augmented Chebyshev expansions for solving the equation of radiative transfer

Three expansion methods are described using Chebyshev polynomials of the first kind for solving the integral form of the equation of radiative transfer in an isotropically scattering, absorbing, and emitting plane-parallel medium. With the aid of symbolic computation, the unknown expansion coefficients associated with this choice of basis functions are shown to permit analytic resolution. A unified and systematic solution treatment is offered using the projection methods of collocation, Ritz-Galerkin, and Weighted-Galerkin, Numerical results are presented contrasting the three expansion methods and comparing them with existing benchmark results. New theoretical results are presented illustrating rigorous error bounds, residual characteristics, accuracy, and convergence rates. 50 refs., 2 figs., 8 tabs